1. (a) Determine the Cartesian equation for the parametric curve defined byx(t) = 5 sin t and y(t) = 12 cos t%3D(b) Determine the equation to the tangent line at t =for the curve defined in4-part(a).(c) Determine the Cartesian coordinates of the polar point (8,3.(d) Determine the polar coordinates for the Cartesian point (-4, 4)(e) Determine the value of t, where the curve given has a horizontal tangent lineand the value of t2 where the curve has a vertical tangent line ifr(t) = t2 – 4t +3y(t) = 8/t – 2tfor 0

We have to find the equation of the curve ,tangent equation to the curve. Note - As per our…

Answered: (a) Determine the Cartesian equation…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter8: Polar Coordinates And Parametric Equations

Section8.CT: Chapter Test

Problem 8CT

See similar textbooks

Similar questions

Find parametric equations for the curve x = 5(y - 1)(y - 2) sin y and then plot the curve using a graphing utility.
a) For the parametric curve x = t^2 + 2t + 1, y = 6t + 1, find the Cartesian equation(s) forall tangent lines to this curve with slope 3. Write your line equation(s) in the point-slope form b) Plot and label the following polar point on the graph.Find the Cartesian coordinates of this point.C = (r, θ) = (4,5π/6) c) Consider the point with Cartesian coordinates (x, y) = (−1,√3)Plot this point in the (x, y)-plane.Find polar coordinates (r, θ) of this point, where r > 0 and 0 ≤ θ ≤ 2π
Consider the curve defined by the parametric equations X = cos t, y = 3sec t on the interval 0sts"/2, Eliminate the parameter, t, to find a Cartesian equation for this curve. Use the equation editor to enter your answer in correct mathematical form.
9. (a) Find the rectangular coordinates of the point(s) of the graph of the polar equation r = 4 sin that are farthest from the y-axis.
Sketch the parametric curve and eliminate the parameter to find the Cartesian equation of the curve x = 3 cos(Θ) , y = sin(Θ)
Find the equation of the tangential line(s) to the given set of parametric equation at the given point.
Find the polar equation for the Cartesian curve x² - y² = r = 1 r sin 20 = 1 r = sec 20 r = cos 20 cos 201 x² + y².
Sketch the plane curve represented by the given parametric equation x = 2 sin t - 3, y = 2 sin t + 1. Then use interval notation to give the relation’s domain and range.
Use the parametric equations x= sec(t) , y=tan(t), for -pi/2 < t < pi/2. Sketch the curve represented by the parametric equations (include the orientation of the curve) and write the corresponding rectangular equation by eliminating the parameter and Find the equation of the tangent line to the curve at t = pi/4
10. (a) Given the polar equation r = -4 cos 0. Write the polar equation as a Cartesian equation. (b) Sketch the curve for 5<0
6. (i) Convert the equation (x – 2)2 + y? = 4 from cartesian to polar (ii) Convert the equation r2 = 4r sin 0 from polar to cartesian.
What curve do the parametric equations x= e', y= e " represent? Find the slope of the tangent line to this curve at the point (3, 9). Find the concavity of the curve at this point.

SEE MORE QUESTIONS

Recommended textbooks for you

Algebra and Trigonometry (MindTap Course List)

Algebra

ISBN:

9781305071742

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Algebra and Trigonometry (MindTap Course List)

Algebra

ISBN:

9781305071742

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

SEE MORE TEXTBOOKS

(a) Determine the Cartesian equation for the parametric curve defined by x(t) = 5 sin t and y(t) = 12 cos t %3D (b) Determine the equation to the tangent line at t = for the curve defined in 4 part(a). (c) Determine the Cartesian coordinates of the polar point (8,